R函数查找适合常数的合适值 [英] R function to find suitable values for fitting constants

问题描述

library(ggplot2)
set.seed(1)
dataset <- data.frame(X = rnorm(1000))
dfun <- function(x, a, b) 1/(sqrt(2*pi)*b)*exp(-0.5*((x-a)^2/(2*b^2))) 
ggplot(dataset, aes(x = X)) + 
  geom_histogram(aes(y = ..density..), binwidth = 0.5)+
  stat_function(fun = dfun,
                args = list(a = , b = ))

在这种情况下，如何计算 a 和 b 的合适值?

How can I calculate suitable values of a and b in case like this?

推荐答案

您可以使用 nls 计算参数 a 和 b 的值.类似于以下内容.

You can compute values for the arguments a and b with nls. Something like the following.

dens <- density(dataset$X, n = nrow(dataset))
df_dens <- data.frame(x = dens$x, y = dens$y)

a0 <- mean(dataset$X)
b0 <- sd(dataset$X)
fit <- nls(y ~ dfun(x, a, b), data = df_dens, start = list(a = a0, b = b0))

coef(fit)
#           a            b 
#-0.007006625   0.97518478 

现在使用 a 和 b 的这些值绘制直方图和函数.

Now plot the histogram and the function with these values for a and b.

ggplot(dataset, aes(x = X)) + 
  geom_histogram(aes(y = ..density..), binwidth = 0.5)+
  stat_function(fun = dfun,
                args = list(a = coef(fit)[1], b = coef(fit)[2]))

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